To demonstrate this, let us consider a simple example in Fig. REF .
Using topological batching to update the two job DAG in the figure
at the same time, and assuming that the average time required for
\(\textit {B}_{j}\)  to be updated once is \(\textit {T}_{0}\) . \(\textit {L}\) 
= 2, is the number of iterations. \(\textit {N}\)  = 3, is the maximum
number of sequential batches in job DAGs. Because Pipelined-DAGNN
use the current-layer, rather than the past-layer, information to
compute the current-layer representation of \(v\)  and aggregates from
the direct-predecessor set \(\mathcal {P}(v)\)  only, rather than the
entire neighborhood [1]}. As shown in Fig. REF ,
\(\textit {B}_{j}^{1}\)  and \(\textit {B}_{j}^{2}\)  respectively represent
the first iteration update and the second iteration update of the
sequential batch \(\textit {B}_{j}\) . The time required for sequential
batch \(\textit {B}_{j}\)  to iteratively update twice is 6\(\textit {T}_{0}\) ,
and considering the pipeline mechanism, when \(\textit {B}_{0}^{1}\) 
ends, \(\textit {B}_{0}^{2}\)  and \(\textit {B}_{1}^{1}\)  can be performed
simultaneously, the time spent is 4\(\textit {T}_{0}\) . It can be inferred
from the figure that the time spent without considering the pipeline
mechanism is \(\textit {N}\times \textit {L}\times \textit {T}_{0}\) . On
the contrary, the time spent is \((\textit {N}-1)\times \textit {T}_{0}+\textit {L}\times \textit {T}_{0}\) .
The acceleration ratio is \(\frac{\textit {L}\times \textit {N}}{\textit {L}+\textit {N}-1}\) .
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